From an employer's perspective, there are two issues:
a) Conflict of interest. Assuming the contract says "no web design work", not "no work fullstop" then then it's not overly restrictive. Anyway, you haven't signed it yet. Negotiate if you want.
b) Conflict of time. I don't really want my employees to spend their down time working at other people's beck and call (i.e. in employment). I want them to turn up to work reasonably refreshed, and having two bosses is not going to help them do this. On the other hand, it's their life, and provided they perform excellently at work, then why should I complain if they want to practice their skills and get paid a bit for it? It may well benefit them,
The worst the employer can do if they find out is
a) fire you, and even then you might have a case for unfair dismissal if your performance was fine, though personally I think you should swallow it and leave.
b) sue you for breach of contract. But they can only sue for actual losses, which would be pretty hard to show unless you were somehow personally responsible for a contract falling through. Pretty hard to prove that one, even to the balance of probabilities required by a civil court.
--EDIT--
Perhaps I didn't make it clear that I am an employer and this isn't just a hypothetical viewpoint. I seem to have been downrated recently for this answer, apparently because people don't like it. It is, however, factual.
Regarding the complaint that it is no business of mine how employees spend their time outside work, I agree. But the commenter apparently didn't notice that I also said "it's their life". My concern is how they perform during working hours, and if their other activities impinge on that, then it is certainly my business.